AIIMS2019Physics-Vectors

AIIMS 2019 Physics Vector Addition MCQ Question

Type: MCQ-conceptual-Medium-Class 11

Assertion: If A+B=AB|\vec{A} + \vec{B}| = |\vec{A} - \vec{B}|, then the angle between A\vec{A} and B\vec{B} is 9090^\circ.

Reason: A+B=B+A\vec{A} + \vec{B} = \vec{B} + \vec{A}

A

If both assertion and reason are true and reason is the correct explanation of assertion.

B

If both assertion and reason are true but reason is not the correct explanation of assertion.

C

If assertion is true but reason is false.

D

If both assertion and reason are false.

Correct Answer

Option A

Detailed Explanation

The equation |𝐀⃗ + 𝐁⃗| = |𝐀⃗ − 𝐁⃗| implies that the magnitudes of the vectors 𝐀⃗ and 𝐁⃗ are equal when the angle θ between them is 90°, leading to the conclusion that 𝐀⃗ and 𝐁⃗ are perpendicular. This relationship confirms the commutative property of vector addition, as 𝐀⃗ + 𝐁⃗ = 𝐁⃗ + 𝐀⃗ holds true regardless of the angle between the vectors. Since the other options are not provided or relevant to the question, they cannot be assessed for correctness. Understanding this concept is fundamental in vector analysis and helps in visualizing the geometric interpretation of vector operations.

Found an issue with this question?